We use Gallery2 on our site (
www.stuypulse.com/gallery). I'd have to say that it's really very powerful and there's tons of plugins for it. In addition, we have it integrated with SMF (although the bridge is quite finicky/buggy). There's probably integration for other user systems as well.
One of the things I like most about it is its mass "facebook-style" photo uploader. However, skinning seems like somewhat of a pain, although its not
that bad.